• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.341-348
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• 1998

In this paper, we show that Schlumprecht space is reflexive and the Dual of Schlumprecht space has the Banach-Saks property and study behavior of block basic sequence in Schlumprecht space.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.237-244
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• 2009

In this paper, we define property ($C_k$) and show that Property ($C_k$) implies property ($C_{k+1}$). The converse does not hold. Moreover, we prove that property ($C_k$) implies the Banach-Saks property.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1017-1030
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• 2005

In this paper, we study averaging properties in Banach spaces using the Brunel-Sucheston's spreading model. We show that the Schlumprecht space S does not have the Banach­Saks property and II is finitely representable in the Schlumprecht space S using the spreading model properties.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.407-416
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• 2008

In this paper, we study property ($B_2$) and property ($D_2$) and their implications.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.161-168
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• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.301-308
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• 2011

In this paper, we define the alternate forms of property ($A_{\kappa}$) and study their implications.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1519-1525
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• 2010

In this paper, we define property ($D_k$) and get the following strict implications. $$(UC){\Rightarrow}(D_2){\Rightarrow}(D_3){\Rightarrow}{\cdots}{\Rightarrow}(D_{\infty}){\Rightarrow}(BS)$$.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.415-422
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• 2012

In this paper, we define the weak property (${\beta}_{\kappa}$) and get the following strict implications. $$(UC){\Rightarrow}w-({\beta}_1){\Rightarrow}w-({\beta}_2){\Rightarrow}\;{\cdots}\;{\Rightarrow}w-({\beta}_{\infty}){\Rightarrow}(BS)$$.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.497-507
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• 2004

In this paper, we first seek the equivalent statements with averaging properties in terms of the regular summability method, secondly define some new averaging properties and study their implications. Finally, we investigate the question of what property is dual to the Banach-Saks property suggested by C. Seifert.